Hi Beard! Welcome! I'm brand new also, and everyone here has been super nice about answering my questions. And now I can pay it forward!

Regarding the type of water to use, from everything I've read here on the boards and other sources, you should never use distilled, filtered or purified water for your Betta. Those waters are missing the nutrients that Bettas need to stay healthy. It seems tap water is the best choice (when used with a dechlorinator like AquaSafe) although bottled water is okay too. I don't know where spring water fits into all of that, however.

It depends on a few factors....
You don't have to buy water for a fish tank, tap water with conditioner is fine. However, if you do have to buy water, I'd say spring. But I would just use tap water instead. Conditioner will last a while too!

Now, it mainly depends on the betta and it's home. As long as the tank is large enough, and heated, conditioned, etc, it could take from a couple days to a week to possibly longer. For me, it's usually been a couple days.

^^And I just had to say this!!! For my careers class in school, we just got done watching the movie "Pay it Forward" lol

Tap water combined with conditioner is your best bet. Distilled is a big no-no and bottled water would be expensive and wasteful.
Every betta is different...so it could be just a few days for your betta to adjust, or maybe even longer. After all, he did just have a big transition! One of my bettas took 2 weeks before he got used to everything. So just let him make himself home at his own pace c: